Bounds on Arithmetic Rainbow Ramsey Multiplicities
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914242737733632 |
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| author | Elvin, Gabriel Gonzales, Alexis Rodriguez, Alejandro Wilbur, Israel |
| author_facet | Elvin, Gabriel Gonzales, Alexis Rodriguez, Alejandro Wilbur, Israel |
| contents | We study a quantitative Ramsey-type problem on 3-term arithmetic progressions: how should the set of integers $[n] = \{1, 2, \dots, n\}$ be colored using 3 colors in order to maximize the number of rainbow 3-term arithmetic progressions? By "rainbow", we mean progressions whose elements are each assigned a distinct color. We determine a lower bound for this question and upper and lower bounds when $[n]$ is replaced with the integers modulo $n$, including an exact maximum when $n$ is a multiple of 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05442 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounds on Arithmetic Rainbow Ramsey Multiplicities Elvin, Gabriel Gonzales, Alexis Rodriguez, Alejandro Wilbur, Israel Combinatorics 05D10 We study a quantitative Ramsey-type problem on 3-term arithmetic progressions: how should the set of integers $[n] = \{1, 2, \dots, n\}$ be colored using 3 colors in order to maximize the number of rainbow 3-term arithmetic progressions? By "rainbow", we mean progressions whose elements are each assigned a distinct color. We determine a lower bound for this question and upper and lower bounds when $[n]$ is replaced with the integers modulo $n$, including an exact maximum when $n$ is a multiple of 3. |
| title | Bounds on Arithmetic Rainbow Ramsey Multiplicities |
| topic | Combinatorics 05D10 |
| url | https://arxiv.org/abs/2601.05442 |